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hgtecdteI am a condensed matter theorist.  My research consists of using ab initio techniques, mainly density functional theory (DFT), to study interesting materials systems. In principle, DFT is an exact way to rewrite the many-body Schrodinger's equation, allowing one to solve for the ground state energy and charge density of a given configuration of atoms; although in practice it requires approximations.  See the wikipedia entry on DFT for more information

Here is a brief introduction to some topics I have previously studied at Rutgers and Yale.  See my publication list for detailed information.

1. Chern insulators (quantum anomalous Hall insulators).

2. High-throughput searches for new functional materials.

3. Oxide Interfaces.

4. Advanced Surface Chemistry.

5. Semiconductor Surfaces.

6. Pseudopotentials


Chern Insulators

At a general level, the properties of most condensed matter systems are determined by their symmetries.  For instance, a material with broken inversion symmetry can have a spontaneous polarization and a first-order response to an electric field. Topological condensed matter systems differ in that some of their properties are determined instead by a bulk topological invariant, which is consists of an integral over k-space of some function of the phase of the wavefunction.  In insulators, these topological invariants are guaranteed to be integers, which allows us to classify insulators by their topology.

While there has been great success in finding 2D and 3D time-reversal invariant topological insulators, the first proposed topological insulators (Haldane 1988), known as Chern insulators or quantum anomalous Hall insulators, are only just now beginning to be studied experimentally.  A Chern insulator, like a system which displays the integer quantum Hall effect, is a system with a non-zero Chern number.  Chern insulators will display many of the interesting properties of the integer quantum Hall effect, including quantized dissipationless spin-polarized edge states, but without the strong external magnetic fields and low temperatures required by the quantum Hall effect.

In order to have a robust non-zero Chern number, a system must have broken time reversal symmetry and strong spin-orbit coupling.  Previous attempts to construct such a combination have largely consisted of doping a time-reversal invariant topologically non-trivial material with magnetic atoms, to push the material into a state with non-trivial Chern number; however these attempts have proven very difficult experimentally.  

We propose instead to directly combine spin-orbit with magnetism by depositing heavy atoms (e.g. Pb) onto the surface of a normal magnetic insulator (e.g. MnTe).  The advantages of this approach are that it does not require doping, it guarantees that the spins are aligned, and it features atoms with the strongest possible spin-orbit coupling.  We have verified this approach using first principles calculations, finding many Chern insulators including some with large band gaps, and we suggest a combined first principles / experimental search to find an experimentally realizable Chern insulator.  See our paper for details.

chern

Figure: Geometry of a proposed Chern insulator.  2/3 ML Pb on A-type antiferromagnetic MnTe.



High-throughput Searches for Functional Materials

Many of the technological challenges facing the world today are in fact materials challenges.  In the energy sector, photovoltaics, batteries, hydrogen strorage, etc., all require better, faster, lighter, and cheaper materials.  Furthermore, pushing beyond the limits of traditional silicon-based field effect transistors and magnetic storage requires new materials which can be used as high-k dielectrics, high-mobility semiconductors, ferroelectrics,  piezoelectrics, multiferroics, etc.

First principles theoretical techniques have advanced to the point that the properties of many materials can be calculated accurately and efficiently, without input from experiment, making these techniques ideal for scanning large numbers of both previously synthesized and novel materials for interesting and useful properties.  In a high-throughput search, the properties of an entire classes of materials can be analyzed in order to find examples which have ideal properties for any given application.  These candidate materials can then be synthesized, characterized, and hopefully applied.

One particularly useful property a material can have is a strong response to an electric field.  A ferroelectric is a material which has a polar ground state, the direction of which can be switched with in an electric field.  Closely related to ferroelectrics are antiferroelectrics, which are materials with an anti-polar ground state; however, they also have a low energy polar state which can be switched to in an electric field.antiferro

Figure: Schematic of antiferroelectrics

Perovskite oxide ferroelectrics and to a lesser extent antiferroelectrics have been studied extensively; however, in many cases their properties are not ideal for applications.  We have used high-throughput techniques to discover and study new classes of ABC semiconducting hexagonal ferroelectrics and antiferroelectrics.  These materials have a variety of advantages over traditional ferroelectrics and antiferroelectrics, including uniaxial polarization, large band gap ranges (including semiconductors), and different shapes and chemistries which should allow them to interface with more materials.  See here and here for more details.

abc

Figure: ABC ferroelectrics and antiferroelectrics

I am also involved in techniques for doing high-throughput calculations, see the section on pseudopotentials.


Oxide Interfaces

Oxides, and in particular perovskite oxides, provide the opportunity for a wide range of functionality, including ferroelectrics, antiferroelectrics, ferromagnets, multiferroics, high-k materials, superconductivity, etc. However, by combining different perovskite oxides, it is possible to achieve even greater functionality, examples of which include 2D electron gases at polar/non-polar interfaces (SrTiO3/LaAlO3) and improper ferroelectricity (see here or here).

I have studied theoretically the coupling of phonons from a SrTiO3 (STO) substrate into a La0.5Sr0.5MnO3 (LSMO) thin film, which was previously grown by the Ahn group at Yale.  When STO goes through its phonon-softening phase transition, its phonons couple strongly to the LSMO, affecting the LSMO's magnetism and conductivity. Based on first principles calculations, I created a classical model of the force-constants in these materials and used finite-temperature Monte Carlo to analyze this effect as a function of temperature.  This type of strong interfacial phonon coupling provides an interesting new probe to study oxide systems. See here for more details.

lsmo/sto

Figure: Top- geometry of LSMO/STO interface.  Bottom- low freqency phonon eigenvector extends into LSMO.


Ferroelectric Surface Chemistry

Ferroelectric materials have a strong, persistent response to an electric field, and their surfaces provide an opportunity to use this response to do advanced chemistry.  For instance, one could bind molecules to the positively-poled surface, encouraging a chemical reaction, and then switch the polarization to release the products. Studying these complicated reactions requires careful analysis of surface thermodynamics and kinetics. As a proof of principle, I have studied the binding of H2O and CO2 to the PbTiO3 surface under positive and negative polarization, finding a variety of changes upon polarization reversal.  See here or our review for more details.

ferro

Figure: Bonding of CO2 to TiO2-terminated PbTiO3 surface.  Electrons move to blue regions due to bonding.


Semiconducting Surfaces


My earliest work consisted of studying the deposition of submonolayer coverages of Sr and La onto Si (001) and Ge (001).  These technologically relevant surfaces are the first step in growing complex oxides on Si. In collaboration with the Ahn group and Altman group at Yale, I determined the structure of the 1/6 ML Sr on Si and Sr on Ge structures.  These structures have been been studied/confirmed experimentally by STM, and understanding these complex surface reconstructions has helped improve oxide growth on semiconductors.  See our review here.


surface

Figure: Structures of submonolayer Sr on semiconducting surfaces.